Quantum Cohomology and Crepant Resolutions: A Conjecture

Tom Coates[1]; Yongbin Ruan[2]

  • [1] Imperial College London Department of Mathematics London SW7 2AZ United Kingdom
  • [2] Department of Mathematics University of Michigan Ann Arbor MI 48105 USA

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 2, page 431-478
  • ISSN: 0373-0956

Abstract

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We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold 𝒳 to the quantum cohomology of a crepant resolution Y of 𝒳 . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus Gromov–Witten invariants of 𝒳 from those of Y .

How to cite

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Coates, Tom, and Ruan, Yongbin. "Quantum Cohomology and Crepant Resolutions: A Conjecture." Annales de l’institut Fourier 63.2 (2013): 431-478. <http://eudml.org/doc/275500>.

@article{Coates2013,
abstract = {We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold $\mathcal\{X\}$ to the quantum cohomology of a crepant resolution $Y$ of $\mathcal\{X\}$. We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus Gromov–Witten invariants of $\mathcal\{X\}$ from those of $Y$.},
affiliation = {Imperial College London Department of Mathematics London SW7 2AZ United Kingdom; Department of Mathematics University of Michigan Ann Arbor MI 48105 USA},
author = {Coates, Tom, Ruan, Yongbin},
journal = {Annales de l’institut Fourier},
keywords = {Quantum cohomology; orbifold; crepant resolution; Gromov–Witten invariants; crepant resolution conjecture; quantum cohomology; Gromov-Witten invariants},
language = {eng},
number = {2},
pages = {431-478},
publisher = {Association des Annales de l’institut Fourier},
title = {Quantum Cohomology and Crepant Resolutions: A Conjecture},
url = {http://eudml.org/doc/275500},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Coates, Tom
AU - Ruan, Yongbin
TI - Quantum Cohomology and Crepant Resolutions: A Conjecture
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 2
SP - 431
EP - 478
AB - We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold $\mathcal{X}$ to the quantum cohomology of a crepant resolution $Y$ of $\mathcal{X}$. We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus Gromov–Witten invariants of $\mathcal{X}$ from those of $Y$.
LA - eng
KW - Quantum cohomology; orbifold; crepant resolution; Gromov–Witten invariants; crepant resolution conjecture; quantum cohomology; Gromov-Witten invariants
UR - http://eudml.org/doc/275500
ER -

References

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